A quantity of \(85.0 \mathrm{~mL}\) of \(0.900 \mathrm{M} \mathrm{HCl}\) is mixed with \(85.0 \mathrm{~mL}\) of \(0.900 \mathrm{M}\) KOH in a constantpressure calorimeter that has a heat capacity of \(325 \mathrm{~J} /{ }^{\circ} \mathrm{C}\). If the initial temperatures of both solutions are the same at \(18.24^{\circ} \mathrm{C},\) what is the final temperature of the mixed solution? The heat of neutralization is \(-56.2 \mathrm{~kJ} / \mathrm{mol} .\) Assume the density and specific heat of the solutions are the same as those for water.

Calorimetry is an experimental technique used to measure the amount of heat absorbed or released during a chemical reaction, phase transition, or physical change. It is a critical component in thermodynamics and provides insight into the energy changes occurring within a system.

The constant pressure calorimeter used in the exercise is a simple version often referred to as a coffee cup calorimeter. It is insulated to prevent heat exchange with the environment and allows reactions to be carried out at constant atmospheric pressure. The calorimeter has its own heat capacity, which indicates the amount of heat needed to raise its temperature by one degree Celsius. This inherent property must be considered along with the heat changes of the solution inside.

When an acid and a base, such as HCl and KOH, are mixed in a calorimeter, the heat of neutralization released or absorbed is transferred to both the solution and the calorimeter. By assuming the density and specific heat of the solution are equivalent to those of water, we simplify the calculations. The final temperature is then determined by considering the initial temperatures and the total heat produced or absorbed during the reaction, which involves the concept of stoichiometry as well.

Stoichiometry is the mathematical relationship between the quantities of reactants and products in a chemical reaction. It is based on the conservation of mass and the balanced chemical equation for the reaction.

In the provided exercise, stoichiometry comes into play when calculating the number of moles of HCl and KOH. By using the given molarity (concentration) and volume, we determine the moles of each reactant that will participate in the acid-base reaction. The balanced equation for the neutralization of HCl with KOH indicates a one-to-one mole ratio between the reactants. This means that an equal number of moles of acid and base will react completely, with no excess.

As the reaction proceeds, stoichiometry helps us understand the quantities involved in the production of heat. For instance, if the reaction releases a specific amount of heat per mole of reacted substance, we can calculate the total heat released by multiplying this heat of neutralization by the total moles of reactants, assuming all moles react.

An acid-base reaction, such as the one occurring between HCl and KOH, is a type of chemical reaction where an acid reacts with a base to produce water and a salt. In this specific context, the acids and bases are defined by the Arrhenius or Brønsted-Lowry theories, where acids donate protons (H+) and bases accept them.

The reaction between HCl (hydrochloric acid) and KOH (potassium hydroxide) can be represented as follows: \[ \mathrm{HCl} (aq) + \mathrm{KOH} (aq) \rightarrow \mathrm{KCl} (aq) + \mathrm{H_2O} (l) \] This neutralization reaction is exothermic, meaning it releases heat. The heat of neutralization is the energy change associated with the formation of one mole of water from the reaction between an equivalent of an acid and a base. For strong acids and bases, this value tends to be fairly constant, typically around -57 kJ/mol for reactions at 25°C occurring in dilute aqueous solutions.

In the context of our exercise, once the number of moles of acid and base is known, and they are mixed in the calorimeter, the total energy change can be calculated using the provided heat of neutralization. The resulting calculation will inform how much the temperature of the solution increases as a result of the acid-base reaction.